Sory to hear your child is not well. It is not uncommon for children to develop these infections when they are little as their immune systems are still immature and slowly developing.
Full blood count done at the time of active infections will show abnormal immunity ('low') as cells are used up to fight the infection. I am not sure what exact test was done but am guessing a lymphocyte count
as part of a full blood count.
If the child attends play school it is even more common to have 'constant' infections.
The important thing to see is the response to antibiotics. If children require intravenous antibiotics, or hospitalisations for pneumonias, or have recurrent ear infections (sinuses are absent until 2years of age, so no sinusitis!) then the absolute lymphocyte count test should be >2. If not, an immune deficiency
should be excluded. Polyps in children are almost synonymous with cystic fibrosis
(proven on sweat tests and confirmed on genetic testing
should be fine as long as she responds.
I hope that was useful.